An elusive trig proof I can't seem to get

[SpecialKM]

1. The problem statement, all variables and given/known data

Prove that:

(sin(x)+ tan(x))/(cos(x)+ 1)= tan(x)

2. Relevant equations

There are just trig identities that we can use.


3. The attempt at a solution
I've attempted every possible way I can think of and it would just look like jibberish here.

[HallsofIvy]

What you wrote, sin(x)+ tan(x)/cos(x)+ 1= tan(x). isn't true! For example, if x= 0, then sin(x)= sin(0)= 0, tan(x)/cos(x)= tan(0)/cos(0)= 0/1= 0 so the left side is 1. But the right side, tan(x)= tan(0), is 0.

What I think you meant was (sin(x)+ tan(x))/(cos(x)+ 1)= tan(x).

If you multiply both sides of the equation by cos(x) you get
(sin(x)cos(x)+ sin(x))/(cos(x)+ 1)= sin(x).

[SpecialKM]

Sorry yeah, that's what I meant, my mistake. I'll change that right now.

[Pi-Bond]

Use the fact that tan(x)=sin(x)/cos(x). The proof should just involve two lines of algebra.

[icystrike]

factor out tan(x) from numerator and u get cos(x)+1 which cancels with denominator